The spectrum problem for abelian \(\ell\)-groups and MV-algebras

DOI10.1007/s00012-020-00668-4zbMath1460.06002arXiv1907.11095OpenAlexW3040263023MaRDI QIDQ776994

Antonio Di Nola, Giacomo Lenzi

Publication date: 13 July 2020

Published in: Algebra Universalis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.11095

zbMATH Keywords

latticepolyhedronprime idealMV-algebraspectral spacereticulationlattice ordered abelian group

Mathematics Subject Classification ID

Heyting algebras (lattice-theoretic aspects) (06D20) Lattices and duality (06D50) MV-algebras (06D35) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20)

Related Items (3)

Reticulation of a quantale, pure elements and new transfer properties ⋮ A solution to the MV-spectrum problem in size aleph one ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The dual adjunction between MV-algebras and Tychonoff spaces
• MV-algebras, infinite dimensional polyhedra, and natural dualities
• Advanced Łukasiewicz calculus and MV-algebras
• Representation theory of MV-algebras
• Interpretation of AF \(C^*\)-algebras in Łukasiewicz sentential calculus
• Farey stellar subdivisions, ultrasimplicial groups, and \(K_ 0\) of AF \(C^*\)-algebras
• Reticulated rings
• On some lattice quotients of \(MV\)-algebras
• Priestley duality and quotient lattices of many-valued algebras
• The monadic theory of order
• Directed colimits of free commutative semigroups
• Groupes et anneaux reticules
• Prime spectra of lattice-ordered abelian groups
• A characterisation of lattice-ordered Abelian groups
• A completely normal spectral space that is not a real spectrum
• Perfect MV-algebras are categorically equivalent to Abelian \(l\)-groups
• Extending Stone duality to multisets and locally finite MV-algebras.
• Tarski's theorem on intuitionistic logic, for polyhedra
• Duality theory and skeleta for semisimple MV-algebras
• Algebraic foundations of many-valued reasoning
• Pro-finite MV-spaces
• The poset of prime \(l\)-ideals of an abelian \(l\)-group with a strong unit
• Convex approximation technique for interacting line elements deblurring: a new approach
• Relative subalgebras of MV-algebras
• On the order of prime ideals
• A Compact [0,1-valued First-order Lukasiewicz Logic with Identity on Hilbert Space]
• Semisimple Algebras of Infinite Valued Logic and Bold Fuzzy Set Theory
• Lattice Theory: Foundation
• Algebraic Analysis of Many Valued Logics
• Generic substitutions
• Dimension Groups and Their Affine Representations
• Applications of Duality in the Theory of Finitely Generated Lattice-Ordered Abelian Groups
• A constructive proof of McNaughton's theorem in infinite-valued logic
• Combinatorial Aspects of Piecewise Linear Functions
• Spectral spaces of countable Abelian lattice-ordered groups
• The Lebesgue state of a unital abelian lattice-ordered group
• Free Vector Lattices
• Prime Ideal Structure in Commutative Rings
• Yosida Type Representation for Perfect MV‐Algebras
• Topological representations of distributive lattices and Brouwerian logics

This page was built for publication: The spectrum problem for abelian \(\ell\)-groups and MV-algebras